p=x^2+54y^2 형태의 소수에 관한 연구A study on the primes of the form p
In this thesis, we generate ring class fields of imaginary quadratic fields in terms of the special values of certain eta-quotients, which are related to the relative norms of Siegel-Ramachandra invariants. These give us minimal polynomials with relatively small coefficients from which we are able to solve the Diophantine equations $p=x^2+ny^2$. In particular, we classify all the primes of the form $x^2+54y^2$.
- Advisors
- Koo, Ja-Kyungresearcher; 구자경
- Description
- 한국과학기술원 : 수리과학과,
- Publisher
- 한국과학기술원
- Issue Date
- 2014
- Identifier
- 592350/325007 / 020124521
- Language
- eng
- Description
학위논문(석사) - 한국과학기술원 : 수리과학과, 2014.8, [ ii, 24 p. ]
- Keywords
class field theory; 지겔-라마찬드라 불변량; 환유체; 에타함수; 시무라의 상호법칙; 유체론; Shimura`s reciprocity law; eta-quotient; ring class field; A study on the primes of the form p=x^2+54y^2
- Appears in Collection
- MA-Theses_Master(석사논문)
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